An Epistemic Rationale For Order Independence

The issue of the order dependence of iterative deletion procedures is well known in the game theory community, and conditions on the dominance concept underlying these procedures have meanwhile been detected which ensure order independence (see, e.g., the criteria of Gilboaet al.(1990) and Apt (2011)). While this kind of research deals with the technical issue whether certain iterative deletion procedures are order independent, or not, our focus is on the normative issue whether there are weighty reasons for applying order-independent iterative deletion procedures to strategic games. We tackle this question from an epistemic perspective and attempt to figure out whether order independence contains some specific epistemic meaning. It turns out that, under fairly general conditions on the choice rules underlying the iterative deletion procedures, their order independence coincides with the epistemic characterization of their solutions by the common belief of choice rule following behavior. Presumably, the most challenging condition of this coincidence is the property of independence of unfavorable acts. We also examine the consequences of two weakenings of this property on our epistemic motivation for order independence. Although the coincidence mentioned above does not hold for both weakenings, there still exist links between the order independence of iterative deletion procedures and their epistemic characterization by the common belief of following the choice rules on which these procedures are based.